Maybe, I agree with you that it's what most likely happened, but Carver's group aren't the only survivors out there, maybe a wandering survivor offered Pete mercy or self defense because he turned. For all we know Christa could've done it if she survived the bandit attack
I agree Carver may have did it. It would make sense, because at the point he was only ever mentioned and seen as a threat. So I wouldn't be surprised if he caused that massacre, just to be shown as a hint that he's still alive.
Also, when Carver comes to the ski lodge, he asks for everyone not present to come out and surrender, except for Pete, so he must have known about Pete's death.
It's very possible he killed Pete, but he also very well may have died and reanimated by the time Carver found him. Could have been disembowled and show as a walker.